Not being a Supreme Court justice, I can only offer an opinion with very little weight behind it. I think that it would sustain a challenge, that a challenge would not succeed in overcoming the requirement that there be unique signatures. In light of what the objective is, it does not impinge the right to be a candidate at all, in no instance whatsoever. It does not touch the right to vote at all. Those are the constitutional rights we're talking about.
Political parties don't have constitutional rights, by the way. They have rights by rebound, such as the right of expression and the right of assembly, but—